Economics - Research Publications

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Further Observations on Chain Ladder Bias

Taylor, Greg ( 2002-01)

The chain ladder forecast (CLF) has previously been shown to be biased upward. The present paper calculates the second order approximation to the magnitude of the bias, ie the Taylor series for the bias truncated at terms involving second order moments of observations. Some order relations between data triangles are obtained with respect to this second order bias. While the prediction error of the CLF, as a predictor of loss reserve, does not have zero mean, it does have zero median under certain circumstances. Some numerical consequences are explored.
Chain Ladder Bias

Taylor, Greg ( 2002-01)

The chain ladder forecast of oustanding losses is known to be unbiased under suitable assumptions. According to these assumptions, claim payments in any cell of a payment triangle are dependent on those from preceding development years of the same accident year. If all cells are assumed stochastically independent, the forecast is no longer unbiased. Section 6 shows that, under very general assumptions, it is biased upward. This result is linked to earlier work on some stochastic versions of the chain ladder.